An Existence Theorem for a Class of Wrinkling Models for Highly Stretched Elastic Sheets

Timothy J. Healey

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arXiv · 2302.07327

An Existence Theorem for a Class of Wrinkling Models for Highly Stretched Elastic Sheets

Timothy J. Healey

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Abstract

We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. Without bending energy, the stored-energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to the plane, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small-bending component of the model is the same as that in the classical von K\'arm\'an model. Here we prove the existence of energy minima for a general class of such models.

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Timothy J. Healey. 2023-02-14. An Existence Theorem for a Class of Wrinkling Models for Highly Stretched Elastic Sheets. https://arxiv.org/abs/2302.07327

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